HardMathematicsHigh School (9–10)Mensuration › Surface Areas and VolumesNumericalConceptualBoard ExamSAT
A cone of height 24 cm is cut by a plane parallel to its base so that the small cone and the…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A cone of height is cut by a plane parallel to its base so that the small cone and the frustum have equal volumes. How far above the base is the cut? Give the answer to two decimal places.
Need a reminder? The key ideaShow
A cone cut by a plane parallel to its base gives a small cone similar to the whole cone. If the small cone has the fraction of the height, it has of the curved surface and of the volume. One litre is . The volume of a melted solid is the same after it is recast.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The scale. , so .
Step 2. The small cone. Its height is .
Step 3. The cut. It is above the base.
Check. The cut is far below the half way height of , as it should be.
Answer: the cut is above the base.
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